Simple Transport Model Research Articles

Soluble Model of a Nonequilibrium Steady State: The Van Kampen Objection and Other Lessons.

A simple model of charge transport is provided by a classical particle in a random potential and a dissipative coupling to the environment. The corresponding nonequilibrium steady state (NESS) can be determined analytically when both the disorder and dissipation are weak. We use it to illuminate some foundational issues in nonequilibrium statistical mechanics. We show that at nonlinear level dissipative response sensitively depends on the system-environment coupling, and the range of validity of the linear response theory is set by this coupling. This validates the Van Kampen objection. We also show that the principle of minimum entropy production does not determine the NESS beyond linear order in the electric field, while entropy maximization fails to produce the correct NESS already at linear order.

Nd Isotopic Equilibration During Channelized Melt Transport Through the Lithosphere: A Feasibility Study Using Idealized Numerical Models

AbstractThis study is motivated by the observed variability in trace element isotopic and chemical compositions of primitive (Si52 wt %) basalts in southwest North America (SWNA) during the Cenozoic transition from subduction to extension. Specifically, we focus on processes that may explain the enigmatic observation that in some localities, basalts with low Ta/Th, consistent with parental melts in a subduction setting, have signatures consistent with continental lithospheric mantle (CLM). In locations with the oldest CLM (Proterozoic and Archean), Cenozoic basalts with low Ta/Th have well below zero. We model channelized magma transport through the CLM using simple 1D transport models to explore the extent to which diffusive and reactive mass exchange can modify Nd isotopic compositions via open system melt‐wallrock interactions. For geologically reasonable channel spacings and volume fractions, we quantify the reactive assimilation rates required for incoming melt with a different than the wall‐rock to undergo a substantial isotopic shift during 10 km channelized melt transport. In the presence of grain boundaries, enhanced diffusion between melt‐rich channels and melt‐poor surrounding rock contributes to isotopic equilibration, however this effect is not enough to explain observations; our models suggest a significant contribution from reactive assimilation of wall‐rock. Additionally our models support the idea that the observed covariability in Ta/Th and in Cenozoic basalts cannot be attributed to transport alone and must also reflect the transition from subduction‐related to extension‐related parental melts in SWNA.

Development of novel osteochondral scaffolds and related in vitro environment with the aid of chemical engineering principles

In tissue engineering, collaboration among experts from different fields is needed to design appropriate cell scaffolds and the required three-dimensional environment. Osteochondral tissue engineering is particularly challenging due to the need to provide scaffolds that imitate structural and compositional differences between two neighboring tissues, articular cartilage and bone, and the required complex biophysical environments for cultivating such scaffolds. This work focuses on two key objectives: first, to develop bilayered osteochondral scaffolds based on gellan gum and bioactive glass and, second, to create a biomimetic environment for scaffold characterization by designing and utilizing novel dual-medium cultivation bioreactor chambers. Basic chemical engineering principles were utilized to help achieve both aims. First, a simple heat transport model based on one-dimensional conduction was applied as a guideline for bilayer scaffold preparation, leading to the formation of a gelatinous upper part and a macroporous lower part with a thin, well-integrated interfacial zone. Second, a novel cultivation chamber was developed to be used in a dynamic compression bioreactor to provide possibilities for flow of two different media, such as chondrogenic and osteogenic. These chambers were utilized for characterization of the novel scaffolds with regard to bioactivity and stability under dynamic compression and fluid perfusion over 14 d, while flow distribution under different conditions was analyzed by a tracer method and residence time distribution analysis.

Modeling Water Transport in Polymer Electrolyte Membrane Electrolyzers Using a One-Dimensional Transport Model

In this work, we present a water transport model to quantify the movement of water across Nafion® membranes in a proton exchange membrane electrolyzer as a function of varying operating conditions and membrane parameters. This physics-based model is based on the three main water transport mechanisms: diffusion, electro-osmotic drag, and pressure-driven flow. Three sets of equations are obtained to model the movement of water on the cathode side – I. Material balances for hydrogen and water in the flow channel (z-direction), II. Water movement across the membrane in the x-direction, and III. Expressions for variable membrane properties to serve as model inputs. The condensation of water at the cathode is also modeled to understand the respective transport contributions from the vapor and liquid phases. The coupled equation sets are solved numerically with appropriate boundary conditions. An analytical solution is also obtained for the governing differential equation for the mole fraction of water in the vapor phase. This study is perhaps the first effort for a detailed physics-based transport model to predict the water transport in the electrolyzer in one dimension using the actual measured values for the physical parameters of the system. The model results are compared with the experimental data available for water transport, and a good agreement is observed over the wide range of current, temperature and pressure differentials. Further, with the help of this simple transport model, the numerical analysis is performed to delineate the effect of electrolyzer operating conditions on the net water transport across the membrane, water condensation at the cathode, individual contribution of the transport fluxes, and electrolyzer design. Finally, the model is exercised to simulate the dependence of water transport as a function of membrane thickness. This confirms the validity of the current approach of using thin reinforced membranes by electrolyzer fabricators. Figure 1

Properties of Hydrogen Species in n‐Type Silicon Deduced from In‐Diffusion Profiles

Reported depth profiles of hydrogen in plasma‐exposed n‐Si samples can be fitted with a simple model of hydrogen transport by negative and neutral species (H− and H0) accompanied by a reversible formation of hydrogen–donor pairs (HD) and by an irreversible production of mobile dimers H2A—in particular by a bulk pairing reaction of the H− and H0 species. Contrary to a complicated behavior of hydrogen found in p‐Si (with multiple independent states for positive ions and passivated boron), the situation in n‐Si appears to be much simpler as only single states for H−, H0, and HD are sufficient for profile reproduction. The parameters deduced from the profiles are the diffusivity of H−, the characteristic electron concentration marking equal contributions of H− and H0 into hydrogen transport, and the diffusivity of H2A dimers (in the available temperature range 120–225 °C).

Congestion Transition on Random Walks on Graphs.

The formation of congestion on an urban road network is a key issue for the development of sustainable mobility in future smart cities. In this work, we propose a reductionist approach by studying the stationary states of a simple transport model using a random process on a graph, where each node represents a location and the link weights give the transition rates to move from one node to another, representing the mobility demand. Each node has a maximum flow rate and a maximum load capacity, and we assume that the average incoming flow equals the outgoing flow. In the approximation of the single-step process, we are able to analytically characterize the traffic load distribution on the single nodes using a local maximum entropy principle. Our results explain how congested nodes emerge as the total traffic load increases, analogous to a percolation transition where the appearance of a congested node is an independent random event. However, using numerical simulations, we show that in the more realistic case of synchronous dynamics for the nodes, entropic forces introduce correlations among the node states and favor the clustering of empty and congested nodes. Our aim is to highlight the universal properties of congestion formation and, in particular, to understand the role of traffic load fluctuations as a possible precursor of congestion in a transport network.

Preliminary Verification of the PHITS Code Applicability to Conversion Efficiency Calculation of Direct Charge Nuclear Battery

A direct charge nuclear battery, or DCNB, is one of the nuclear batteries based on direct energy conversion and is characterized by exceptional high voltage generation and conversion efficiency higher than other nuclear batteries. For studying potential applications of DCNB, a preliminary estimation of DCNB electrical power and performance is required; hence, conversion efficiency analysis is crucial. For preliminary verification purposes, an ideal DCNB conversion efficiency was calculated under the simplified electron transport model by using the general-purpose Monte Carlo particle transport calculation code PHITS. The result was compared with a reference experimental efficiency for a T-loaded parallel plate DCNB, and the resulting relative error was approximately 12%. Considering the relative error of 20% or less in DCNB conversion efficiency shown by preceding studies, the resulting error was comparable, and it was concluded that the PHITS code is sufficiently applicable to DCNB conversion efficiency analysis.

A reduced-order model to estimate first wall particle and heat fluxes for systems codes

Current systems codes (SCs) do not assess the impact of plasma filament parameters and dynamics in the SOL when performing systems-level analyses. Simulation tools based on simplified turbulent transport models could address such need, such as the TOKES code, but these tend to run in timescales that are prohibitive for incorporation in SCs. This work presents a technique to build surrogate models for SCs, obtained with the modes of Reduced-Order Models (ROMs), and is exemplified with results from TOKES. These surrogates were developed with Principal Components Analysis (PCA), multivariate regression against TOKES inputs (filament temperatures, densities, and ejection speeds) and k-fold cross-validation, applied to the results after transformations based on rational powers of the inputs to optimize the prediction capabilities of the surrogates. Selection was performed with a modified Kullback-Leibler Divergence (KLD), and validation, with withheld cases. Main results include validation of the methodology due to the relatively low number of modes needed to represent more than 90% of the data variance, and the data transformation exponents that optimize the regression.

The Second-Order Features Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems (2nd-FASAM-L): Mathematical Framework and Illustrative Application to an Energy System

The Second-Order Features Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems (abbreviated as “2nd-FASAM-L”), presented in this work, enables the most efficient computation of exactly obtained mathematical expressions of first- and second-order sensitivities of a generic system response with respect to the functions (“features”) of model parameters. Subsequently, the first- and second-order sensitivities with respect to the model’s uncertain parameters, boundaries, and internal interfaces are obtained analytically and exactly, without needing large-scale computations. Within the 2nd-FASAM-L methodology, the number of large-scale computations is proportional to the number of model features (defined as functions of model parameters), as opposed to being proportional to the number of model parameters. This characteristic enables the 2nd-FASAM-L methodology to maximize the efficiency and accuracy of any other method for computing exact expressions of first- and second-order response sensitivities with respect to the model’s features and/or primary uncertain parameters. The application of the 2nd-FASAM-L methodology is illustrated using a simplified energy-dependent neutron transport model of fundamental significance in nuclear reactor physics.

MALTA: A Zonally Averaged Global Atmospheric Transport Model for Long‐Lived Trace Gases

AbstractWe present a two‐dimensional, zonally averaged global model of atmospheric transport named MALTA: Model of Averaged in Longitude Transport in the Atmosphere. It aims to be accessible to a broad community of users, with the primary function of quantifying emissions of greenhouse gases and ozone depleting substances. The model transport is derived from meteorological reanalysis data and flux‐gradient experiments using a three‐dimensional transport model. Atmospheric sinks are prescribed loss frequency fields. The zonally averaged model simulates important large‐scale transport features such as the influence on trace gas concentrations of the quasi‐biennial oscillation and variations in inter‐hemispheric transport rates. Stratosphere‐troposphere exchange is comparable to a three‐dimensional model and inter‐hemispheric transport is faster by up to 0.3 years than typical transport times of three‐dimensional models, depending on the metric used. Validation of the model shows that it can estimate emissions of CFC‐11 from an incorrect a priori emissions field well using three‐dimensional (3D) mole fraction fields generated using a different 3D model than which the flux gradient relationships were derived. The model is open source and is expected to be applicable to a wide range of studies requiring a fast, simple model of atmospheric transport and chemical processes for estimating associated emissions or mole fractions.

Firebrand burning under wind: an experimental study

Background Spot fires play a significant role in the rapid spread of wildland and wildland–urban interface fires. Aims This paper presents an experimental and modelling study on the flaming and smouldering burning of wood firebrands under forced convection. Methods The firebrand burning experiments were conducted with different wind speeds and firebrand sizes. Key results The burning rate of firebrands under forced convection is quantified by wood pyrolysis rate, char oxidation rate and a convective term. The firebrand projected area is correlated with firebrand diameter, char density, wind speed, and flaming or smouldering burning. A surface temperature model is derived in terms of condensed-phase energy conservation. We finally establish a simplified firebrand transport model based on the burning rate, projected area and surface temperature of firebrands. Conclusion The mass loss due to wood pyrolysis is much greater than that due to char oxidation in self-sustaining burning. The burning rate is proportional to U1/2, where U is wind speed. The projected area for flaming firebrands decreases more rapidly than that for smouldering ones. The firebrand surface temperature is mainly determined by radiation. Implications Knowledge about firebrand burning characteristics is essential for predicting the flight distance and trajectory in firebrand transport.

Modeling water transport in polymer electrolyte membrane electrolyzers using a one-dimensional transport model

In this paper, we present a one-dimensional transport model for water transport across Nafion® membranes in a proton exchange membrane electrolyzer. This physics-based model is based on the three main water transport mechanisms: diffusion, electro-osmotic drag, and pressure-driven flow. A good agreement is obtained between the model predictions using the measured values of the physical parameters as inputs and the previously reported experimental data. Further, with the help of this simple transport model, the numerical analysis is performed to delineate the effect of electrolyzer operating conditions on the net water transport across the membrane, water condensation at the cathode, individual contribution of the transport fluxes, and electrolyzer design. Finally, the model is exercised to simulate the dependence of water transport as a function of membrane thickness. This confirms the validity of the current approach of using thin reinforced membranes by electrolyzer fabricators.

Development and application of a predictive model for advanced tokamak scenario design

Advanced tokamak (AT) scenarios applying additional heating during the current ramp (early-heating) usually require many iterations if developed fully empirically. To reduce the required experimental time, a model has been developed in the ASTRA framework, capable of doing predictive simulations of the relevant parameters. As scenario development requires fast iterations and inter-discharge runs, a sufficiently short run-time is required. While using a simplified transport model to achieve this, comparisons to experimental data from ASDEX-Upgrade (AUG) still show good agreement. Using this model, a new high performance early-heating AT scenario has been developed and successfully run on AUG with the results matching the predictions.

Non-Maxwellian electron effects on the macroscopic response of a Hall thruster discharge from an axial–radial kinetic model

A 2D axial–radial particle-in-cell (PIC) model of a Hall thruster discharge has been developed to analyze (mainly) the fluid equations satisfied by the azimuthally-averaged slow dynamics of electrons. Their weak collisionality together with a strong interaction with the thruster walls lead to a non-Maxwellian velocity distribution function (VDF). Consequently, the resulting macroscopic response differs from a conventional collisional fluid. First, the gyrotropic (diagonal) part of the pressure tensor is anisotropic. Second, its gyroviscous part, although small, is relevant in the azimuthal momentum balance, where the dominant contributions are orders of magnitude lower than in the axial momentum balance. Third, the heat flux vector does not satisfy simple laws, although convective and conductive behaviors can be identified for the parallel and perpendicular components, respectively. And fourth, the electron wall interaction parameters can differ largely from the classical sheath theory, based on near Maxwellian VDF. Furthermore, these effects behave differently in the near-anode and near-exit regions of the channel. Still, the profiles of basic plasma magnitudes agree well with those of 1D axial fluid models. To facilitate the interpretation of the plasma response, a quasiplanar geometry, a purely-radial magnetic field, and a simple empirical model of cross-field transport were used; but realistic configurations and a more elaborate anomalous diffusion formulation can be incorporated. Computational time was controlled by using an augmented vacuum permittivity and a stationary depletion law for neutrals.

Coupled hydro-mechanical model for partially saturated soils based on Cam-Clay plasticity

This paper presents a numerical model of coupled hydro-mechanical behaviour of partially saturated soils. The model is based on Bishop's effective stress concept and the Cam-Clay model, with the compression stiffness influenced by the effect of partial saturation. The mechanical model is accompanied by the simplified water transport model where the water pressure is the only variable and van Genuchten moisture retention curve was adopted. The governing equations are discretized in the framework of the finite element method, and the resulting model is implemented in the in-house open source software package SIFEL. To improve convergence of the Newton-Raphson method used at the global level of the equilibrium finding, the algorithmic stiffness matrix was derived for the used stress return algorithm. A numerical examples of foundation problem illustrates the effective application of the model and proved that the model can capture wetting collapse.

Integrated model control simulations of the electron density profile and the implications of using multiple discrete pellet injectors for control

Pellet injection is regarded as the only realistic actuator for core density control in future reactors such as ITER and DEMO. However, a control strategy that can reliably regulate the plasma close to operational limits using multiple pellet injectors is not yet available. In this paper, we present the first integrated model control simulations where a dedicated model-predictive controller is included in JINTRAC. We show that, when continuous actuators are considered, a simple transport model with a steady-state disturbance rejection paradigm is capable of capturing the particle transport dynamics for multiple transport models and scenarios. This in turn allows the model-predictive controller to deal with the uncertainty and minimize the control error given the limited actuation space. Furthermore, we show that for ITER and DEMO relevant pellet sizes, the discrete, nonlinear dynamics of pellet injection will limit the control performance and jeopardize the constraints if not accounted for by the controller. Hence, we conclude that for high-performance control on future reactors, controllers will have to be developed that explicitly deal with the discrete pellet dynamics.

Comparative C, N, and S cycling along a Californian grassland chronosequence

Carbon (C), nitrogen (N), and sulfur (S) are elements strongly influenced by biological cycling and redox reactions in soils, but few comparative analyses have investigated the behaviors of these elements with time. Thus, we examined changes in content and isotope composition of soil profiles along a chronosequence (58–212 kyr) of marine terraces on the central California coast, in an area with significant background geochemical research. Unlike in other chronosequences in more humid locations, the total C, N, and S in these soils did not vary strongly with age, possibly due to the retention of phosphorus (P). The total pools of soil N and S cannot be explained by wet deposition of NO3 and SO4 alone, suggesting other sources of atmospheric inputs such as NH4+ and dimethyl sulfide. Total C and N declined in a characteristic logarithmic pattern with depth, while S did not. The ratio of extractable soil nitrate (NO3) to total N declined with depth, suggesting strong biological demand via various avenues. In contrast, the ratio of extractable sulfate (SO4) to total S increased with depth, suggesting that S was in biological excess. We used a simple reactive transport model to integrate the depth profiles of total C and N and their isotope values. The depth trends of total concentrations suggested one-pool residence times of approximately 500 to 1000 y, consistent with turnover times calculated by mass balance. Depth trends of stable isotope values indicated that N is isotopically fractionated at a magnitude twice that of C, consistent with observed 15N-depleted nitrous oxide (N2O) emissions during the dry summer months. The isotope composition of S (total and SO4) suggests some isotope enrichment during biogeochemical cycling, but far less than observed for N. Thus, despite significant chemical weathering and elemental loss over time, the biogeochemical cycles of C, N, and S remain relatively unaffected by soil age in this climatic setting.

Moisture absorption of an aerogel-based coating system under different wetting scenarios

Aerogel-based coating mortars (ACM-systems) provide energy-efficient retrofitting solutions for masonry buildings, with thermal conductivities (30–50 mW/(m·K)) comparable to traditional insulation materials. However, limited knowledge on their moisture absorption under rainwater wetting hinders the moisture-safe design of building envelopes incorporating these mortars. Thus, this study investigated the moisture absorption of an ACM-system under three laboratory-created wetting scenarios. A small-scale setup was developed to simulate runoff wetting based on typical wind-driven rain intensities in Sweden, enabling continuous monitoring of moisture conditions during wetting and drying. Two complementary capillary suction experiments under zero (free suction) and elevated hydrostatic pressure explored additional wetting scenarios. The impact of water-repellent paint and surface cracks was also assessed, as previous testing focused on undamaged ACM-systems. Among the three wetting scenarios, runoff wetting resulted in the lowest moisture absorption by the undamaged ACM-system. Water-repellent paint (sd = 0.01 m) reduced moisture uptake by up to 15% during runoff and 50% during free capillary suction for the same system. Horizontal or vertical surface cracks of 1 ± 0.5 mm width increased water absorption by 3–5 times during prolonged runoff wetting, comparable to suction at elevated hydrostatic pressure. Furthermore, a trial was done to verify a simplified numerical moisture transport model using the runoff experiment. The results highlighted the necessity for future model refinement and advanced moisture transport modeling in the ACM-system. The developed small-scale setup facilitated easy use and real-time monitoring of moisture conditions during wetting and drying. Future development should include wind-driven rain simulation alongside the existing runoff wetting scenario.

A local stress criterion to assess the effects of hydrogen embrittlement on the fracture strength of notched tensile specimens

This work addresses the applicability of a local criterion incorporating the coupling of critical stress and a critical hydrogen concentration to predict hydrogen embrittlement effects on the fracture strength of high strength steels using notched round specimens with different notch root radii. The numerical simulations incorporating a relatively simple hydrogen transport model provide strong support for the adoption of a failure criterion in terms of achieving a critical level of tensile stress coupled to the local hydrogen concentration, which, in turn, enable the construction of a failure locus for the degraded material. For the cases analyzed here, construction of such a failure locus based on a critical combination of maximum principal stress and hydrogen concentration enabled predictions of fracture strength for hydrogen-charged tensile specimens which are in very good agreement with experimental data. Overall, the results presented here lend additional support for further developments of a local stress-based criterion to predict hydrogen embrittlement effects on the fracture strength of high strength steels.

Development of compact tokamak fusion reactor use cases to inform future transport studies

The OMFIT STEP (Meneghini et al., Nucl. Fusion, vol. 10, 2020, p. 1088) workflow has been used to develop inductive and steady-state H-mode core plasma scenario use cases for a $B_0 = 8 \, {\rm T}$ , $R_0 = 4 \, {\rm m}$ machine to help guide and inform future higher-fidelity studies of core transport and confinement in compact tokamak reactors. Both use cases are designed to produce 200 MW or more of net electric power in an up-down symmetric plasma with minor radius $a = 1.4 \, {\rm m}$ , elongation $\kappa = 2.0$ , triangularity $\delta = 0.5$ and effective charge $Z_{{\rm eff}} \simeq 2$ . Additional considerations based on the need for compatibility of the core with reactor-relevant power exhaust solutions and external actuators were used to guide and constrain the use case development. An extensive characterization of core transport in both scenarios is presented, the most important feature of which is the extreme sensitivity of the results to the quantitative stiffness level of the transport model used as well as the predicted critical gradients. This sensitivity is shown to arise from different levels of transport stiffness exhibited by the models, combined with the gyroBohm-normalized fluxes of the predictions being an order of magnitude larger than other H-mode plasmas. Additionally, it is shown that although heating in both plasmas is predominantly to the electrons and collisionality is low, the plasmas remain sufficiently well coupled for the ions to carry a significant fraction of the thermal transport. As neoclassical transport is negligible in these conditions, this situation inherently requires long-wavelength ion gyroradius-scale turbulence to be the dominant transport mechanism in both plasmas. These results are combined with other basic considerations to propose a simple heuristic model of transport in reactor-relevant plasmas, along with simple metrics to quantify coupling and core transport properties across burning and non-burning plasmas.